Vortex dynamics on a cylinder

Abstract

Point vortices on a cylinder (periodic strip) are studied geometrically. The Hamiltonian formalism is developed, a non-existence theorem for relative equilibria is proved, equilibria are classified when all vorticities have the same sign, and several results on relative periodic orbits are established, including as corollaries classical results on vortex streets and leapfrogging.

arXiv commentLaTeX2e, 13 pages, 5 figures

References in corpus (1)

• Point vortices on the sphere: a case with opposite vorticities

Cited by in corpus (8)

• Relative Periodic Solutions Of The N-Vortex Problem Via The Variational Method
• The N-vortex Problem on a Riemann Sphere
• Periodic Vortex Streets and Complex Monodromy
• Vortex Dynamics in Tubular Fluid Membranes
• Dynamics of poles with position-dependent strengths and its optical analogues
• Mathematical justification of the point vortex dynamics in background fields on surfaces as an Euler-Arnold flow
• Dynamics of Vortex Clusters on a Torus
• A Hamiltonian approach for point vortices on non-orientable surfaces